Analyzing Cancer Survival Times Using the Exponentiated Fréchet-Gompertz Distribution

Abstract

Understanding the survival of cancer patients is essential for determining optimal treatment strategies. This research introduces a robust distribution for analyzing survival data known as the Exponential Fr ́echet-Gompertz distribution (EFG). The EFG combines the unique characteristics of the Exponential Fr ́echet and Gompertz distributions, enhancing its efficiency and providing greater flexibility in representing complex datasets. The study specifically investigates the EFG distribution’s effectiveness in modeling cancer patients’ survival times. A comprehensive analysis of the distribution’s properties is presented, including the quantile and quartile functions, shape indices, moments, moment-generating function, characteristic function, mean residual life, mean waiting time, R ́enyi entropy, and order statistics. The parameters of the distribution are derivedusing five distinct methods: Maximum Likelihood Estimation (MLE), Ordinary Least Squares (OLS), Weighted Least Squares (WLS), Cram ́er-von Mises (CVM), and Maximum Product of Spacings (MPS). A Monte Carlo simulation technique is employed to evaluate the performance of these estimation methods. The simulation results indicate that as sample size increases, the meansquare error (MSE) values for all estimators decrease. Notably, the MLE exhibits the lowest MSE, while the MPS has the highest MSE, particularly for smaller sample sizes. Furthermore, the study presents a comprehensive comparison of the effectiveness of these estimation methods in analyzing survival times for various cancer types, including bladder, bone, blood and brain cancer. The results indicate that the EFG distribution is an optimal model for representing the survival times of patients across these different cancers data. Furthermore, the W.LS method yielded superior estimations for most datasets concerning cancer patient survival. Overall, the EFG distribution demonstrates exceptional capability in accurately fitting survival times for cancer patients compared to other competing distributions.